Online citations, reference lists, and bibliographies.

Polynomial Relations Between Matrices Of Graphs

Sam Spiro
Published 2019 · Mathematics, Computer Science
Cite This
Download PDF
Analyze on Scholarcy
We derive a correspondence between the eigenvalues of the adjacency matrix $A$ and the signless Laplacian matrix $Q$ of a graph $G$ when $G$ is $(d_1,d_2)$-biregular by using the relation $A^2=(Q-d_1I)(Q-d_2I)$. This motivates asking when it is possible to have $X^r=f(Y)$ for $f$ a polynomial, $r>0$, and $X,\ Y$ matrices associated to a graph $G$. It turns out that, essentially, this can only happen if $G$ is either regular or biregular.
This paper references

Semantic Scholar Logo Some data provided by SemanticScholar